A technique has been developed which enables the calculation of resistive particle wake effects. The technique can simply be calculated to any order, and is easy and quick to evaluate. No assumptions are made about the range of the interaction, but this is especially useful for short range effects. We show how the exact evaluation compares with various common approximations for some simple cases, and implement the technique in the Merlin and PLACET simulation programs. The extension from cylindrical to rectangular apertures is highlighted.